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						<span>Sum of Prime Numbers</span>
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							<span class="ipsType_light"><time datetime="2023-07-05T11:59:12Z" title="07/05/23 11:59  AM" data-short="Jul 5">July 5, 2023</time> in <a href="https://www.scienceforums.net/forum/45-brain-teasers-and-puzzles/">Brain Teasers and Puzzles</a></span>
						
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			<a href="https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/?do=findComment&amp;comment=1244394" rel="nofollow" class="ipsType_blendLinks">Posted <time datetime="2023-07-05T14:21:44Z" title="07/05/23 02:21  PM" data-short="Jul 5">July 5, 2023</time></a>
			
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			Consider the set of integers 2, 3 ... 99. After removal of the first two primes (2, 3) we are left with 96 members, 48 of which are divisible by 2, leaving 48, of which a further 16 are divisible by 3. The remaining 32 plus the members 2 &amp; 3 leave a maximum of 34 potential primes less than 100. Therefore, at least 134 primes &lt;1000 are greater than 100. The sum of these must exceed 13,400 therefore option (A) is false.
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			Of the 168 total, 167 of these are odd numbers and sum to an odd number. Therefore options (C) &amp; (D) are both false.
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			Only option (B) survives.&nbsp;
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	<strong>Edited <time datetime="2023-07-05T14:40:48Z" title="07/05/23 02:40  PM" data-short="Jul 5">July 5, 2023</time> by sethoflagos</strong>
	
	
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			<p>
	You are correct, +1.
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<p>
	<s>Would you please use the "Spoiler" feature next time, to give others a chance?</s>
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	&nbsp;
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		<p>
			The first part can be made shorter: the sum of first 168 integers is 168*169/2 = 14196. This immediately eliminates option A.
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	&nbsp;
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	<strong>Edited <time datetime="2023-07-05T14:46:17Z" title="07/05/23 02:46  PM" data-short="Jul 5">July 5, 2023</time> by Genady</strong>
	
	
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			<blockquote class="ipsQuote" data-ipsquote="" data-ipsquote-contentapp="forums" data-ipsquote-contentclass="forums_Topic" data-ipsquote-contentcommentid="1244397" data-ipsquote-contentid="131993" data-ipsquote-contenttype="forums" data-ipsquote-timestamp="1688567744" data-ipsquote-userid="144555" data-ipsquote-username="Genady" id="ips_uid_5701_5">
	 	<div class="ipsQuote_citation ipsQuote_open">		<a href="#" data-action="toggleQuote" aria-label="Toggle Quote">&nbsp;</a>					<a class="ipsPos_right" href="//www.scienceforums.net/?app=core&amp;module=system&amp;controller=content&amp;do=find&amp;content_class=forums_Topic&amp;content_id=131993&amp;content_commentid=1244397"><i class="fa fa-share"></i></a>				On 7/5/2023 at 10:35 PM,  	<a href="//www.scienceforums.net/?app=core&amp;module=members&amp;controller=profile&amp;id=144555" data-ipshover="" data-ipshover-target="//www.scienceforums.net/?app=core&amp;module=members&amp;controller=profile&amp;id=144555&amp;do=hovercard">Genady</a> said:	</div>

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			Would you please use the "Spoiler" feature next time, to give others a chance?
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<p>
	Apologies.&nbsp;<s>Not aware there was one. Where do I find it?</s>
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	Done.
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	<strong>Edited <time datetime="2023-07-05T14:42:11Z" title="07/05/23 02:42  PM" data-short="Jul 5">July 5, 2023</time> by sethoflagos</strong>
	
	
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			<a href="https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/?do=findComment&amp;comment=1244399" rel="nofollow" class="ipsType_blendLinks">Posted <time datetime="2023-07-05T14:41:14Z" title="07/05/23 02:41  PM" data-short="Jul 5">July 5, 2023</time></a>
			
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			<blockquote class="ipsQuote" data-ipsquote="" data-ipsquote-contentapp="forums" data-ipsquote-contentclass="forums_Topic" data-ipsquote-contentcommentid="1244398" data-ipsquote-contentid="131993" data-ipsquote-contenttype="forums" data-ipsquote-timestamp="1688567979" data-ipsquote-userid="119538" data-ipsquote-username="sethoflagos" id="ips_uid_5701_6">
	 	<div class="ipsQuote_citation ipsQuote_open">		<a href="#" data-action="toggleQuote" aria-label="Toggle Quote">&nbsp;</a>					<a class="ipsPos_right" href="//www.scienceforums.net/?app=core&amp;module=system&amp;controller=content&amp;do=find&amp;content_class=forums_Topic&amp;content_id=131993&amp;content_commentid=1244398"><i class="fa fa-share"></i></a>				On 7/5/2023 at 10:39 PM,  	<a href="//www.scienceforums.net/?app=core&amp;module=members&amp;controller=profile&amp;id=119538" data-ipshover="" data-ipshover-target="//www.scienceforums.net/?app=core&amp;module=members&amp;controller=profile&amp;id=119538&amp;do=hovercard">sethoflagos</a> said:	</div>

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		<p>
			Apologies. Not aware there was one. Where do I find it?
		</p>
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</blockquote>

<p>
	It is the "eye" icon above on the very right.
</p>
<blockquote class="ipsQuote" data-ipsquote="" data-ipsquote-contentapp="forums" data-ipsquote-contentclass="forums_Topic" data-ipsquote-contentcommentid="1244398" data-ipsquote-contentid="131993" data-ipsquote-contenttype="forums" data-ipsquote-timestamp="1688567979" data-ipsquote-userid="119538" data-ipsquote-username="sethoflagos" id="ips_uid_5701_7">
	 	<div class="ipsQuote_citation ipsQuote_open">		<a href="#" data-action="toggleQuote" aria-label="Toggle Quote">&nbsp;</a>					<a class="ipsPos_right" href="//www.scienceforums.net/?app=core&amp;module=system&amp;controller=content&amp;do=find&amp;content_class=forums_Topic&amp;content_id=131993&amp;content_commentid=1244398"><i class="fa fa-share"></i></a>				On 7/5/2023 at 10:39 PM,  	<a href="//www.scienceforums.net/?app=core&amp;module=members&amp;controller=profile&amp;id=119538" data-ipshover="" data-ipshover-target="//www.scienceforums.net/?app=core&amp;module=members&amp;controller=profile&amp;id=119538&amp;do=hovercard">sethoflagos</a> said:	</div>

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		<p>
			Done.
		</p>
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</blockquote>

<p>
	Thank you.
</p>


			
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			<blockquote class="ipsQuote" data-ipsquote="" data-ipsquote-contentapp="forums" data-ipsquote-contentclass="forums_Topic" data-ipsquote-contentcommentid="1244379" data-ipsquote-contentid="131993" data-ipsquote-contenttype="forums" data-ipsquote-timestamp="1688558352" data-ipsquote-userid="144555" data-ipsquote-username="Genady" id="ips_uid_5701_8">
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			I've stumbled upon this puzzle and immediately thought of <a contenteditable="false" data-ipshover="" data-ipshover-target="https://www.scienceforums.net/profile/1135-trurl/?do=hovercard" data-mentionid="1135" href="https://www.scienceforums.net/profile/1135-trurl/" rel="">@Trurl</a>&nbsp; because they post about prime numbers often. Of course, others are welcome to try it as well.
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			As you add primes, you alternate between odd and even sums...5,10,17,28,41...and so on.&nbsp; &nbsp;So you will end the addition process on an odd number, so C and D are out.&nbsp; And A is too small, even just summing the first 168 integers will yield a larger number.&nbsp; So B.
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			Thanks, that was fun.
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					As you add primes, you alternate between odd and even sums...5,10,17,28,41...and so on.&nbsp; &nbsp;So you will end the addition process on an odd number, so C and D are out.&nbsp; And A is too small, even just summing the first 168 integers will yield a larger number.&nbsp; So B.
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					Thanks, that was fun.
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	Correct, and glad you liked it. +1
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            "url": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244397",
            "author": {
                "@type": "Person",
                "name": "Genady",
                "image": "https://www.scienceforums.net/applications/core/interface/email/default_photo.png",
                "url": "https://www.scienceforums.net/profile/144555-genady/"
            },
            "dateCreated": "2023-07-05T14:35:44+0000",
            "text": "You are correct, +1.\n \n\n\n\tWould you please use the \"Spoiler\" feature next time, to give others a chance?\n \n\n\n\t\u00a0\n \n\n\n\n\n\t\u00a0\n \n",
            "upvoteCount": 0
        },
        {
            "@type": "Comment",
            "@id": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244398",
            "url": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244398",
            "author": {
                "@type": "Person",
                "name": "sethoflagos",
                "image": "https://www.scienceforums.net/uploads/profile/photo-thumb-119538.jpg",
                "url": "https://www.scienceforums.net/profile/119538-sethoflagos/"
            },
            "dateCreated": "2023-07-05T14:39:39+0000",
            "text": "Apologies.\u00a0Not aware there was one. Where do I find it?\n \n\n\n\tDone.\n \n",
            "upvoteCount": 0
        },
        {
            "@type": "Comment",
            "@id": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244399",
            "url": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244399",
            "author": {
                "@type": "Person",
                "name": "Genady",
                "image": "https://www.scienceforums.net/applications/core/interface/email/default_photo.png",
                "url": "https://www.scienceforums.net/profile/144555-genady/"
            },
            "dateCreated": "2023-07-05T14:41:14+0000",
            "text": "It is the \"eye\" icon above on the very right.\n \n\n\n\n\tThank you.\n \n",
            "upvoteCount": 0
        },
        {
            "@type": "Comment",
            "@id": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244418",
            "url": "https://www.scienceforums.net/topic/131993-sum-of-prime-numbers/#comment-1244418",
            "author": {
                "@type": "Person",
                "name": "Genady",
                "image": "https://www.scienceforums.net/applications/core/interface/email/default_photo.png",
                "url": "https://www.scienceforums.net/profile/144555-genady/"
            },
            "dateCreated": "2023-07-05T19:12:44+0000",
            "text": "Correct, and glad you liked it. +1\n \n",
            "upvoteCount": 0
        }
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